Sorry, I should have been more specific
The perl script I am trying to start from a submit button, creates
text files based on data read from a database, then saves these files to disk.
Its output just prints 'RUNNING', and 'COMPLETE' to STDOUT,
which in this case needs to be an HTML form so that I know
the status of the perl script

which in this case needs to be an HTML form so that I know the status of the perl script

First, output 512 bytes to make browsers render. Some browsers will never render until the page is loaded completely (like Konqueror), but this works with at least Mozilla and MSIE.
Then, start outputting.

It's a very good idea to set $| to 1, to avoid all buffering. You could use javascript to make it look good.